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An approximation for the volume of a thin spherical shell is the surface area of the inner sphere multiplied by the thickness t of the shell: [2] V ≈ 4 π r 2 t , {\displaystyle V\approx 4\pi r^{2}t,}
In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere (forming a great circle ), so that the height of the cap is equal to the radius of the sphere, the spherical ...
The volume of the n-ball () can be computed by integrating the volume element in spherical coordinates. The spherical coordinate system has a radial coordinate r and angular coordinates φ 1, …, φ n − 1, where the domain of each φ except φ n − 1 is [0, π), and the domain of φ n − 1 is [0, 2 π). The spherical volume element is:
A solid, spherically symmetric body can be modeled as an infinite number of concentric, infinitesimally thin spherical shells. If one of these shells can be treated as a point mass, then a system of shells (i.e. the sphere) can also be treated as a point mass. Consider one such shell (the diagram shows a cross-section):
A spherical Gaussian surface is used when finding the electric field or the flux produced by any of the following: [3] a point charge; a uniformly distributed spherical shell of charge; any other charge distribution with spherical symmetry; The spherical Gaussian surface is chosen so that it is concentric with the charge distribution.
Uniformly initiated spherical charge imploding an inner mass - spherical shell explosive charge of mass C, outer tamper layer of mass N, and inner imploding spherical flyer shell of mass M A special case is a hollow sphere of explosives, initiated evenly around its surface, with an outer tamper and inner hollow shell which is then accelerated ...
The shell of an adult Tonna tessellata can be as large as 45–150 millimetres (1.8–5.9 in). It is a relatively thin and light weight shell, nearly spherical. The body whorl is inflated, with a very wide aperture. Surface is white, smooth and glossy, with distinctive brown-red markings and sculptured by thick spiral ribs. It lacks the operculum.
The volume ratio is maintained when the height is scaled to h' = r √ π. 3. Decompose it into thin slices. 4. Using Cavalieri's principle, reshape each slice into a square of the same area. 5. The pyramid is replicated twice. 6. Combining them into a cube shows that the volume ratio is 1:3.